question_answer 1)

Find the distance of the point (?1, ?5, ?10) from the point of intersection of the line        and the plane          

Answer:

The Cartesian equations of a line and the plane are                      ?. (1)       and x ?y + z = 5                  ?.. (2)       The coordinates of any point on line (1) are       P(3 + 2, 4 ? 1, 2 + 2).       If it lies on the plane (2), then       3 + 2 ? (4 ? 1) + 2 + 2 = 5.                coordinate of point of intersection of line and plane is       (3 × 0 + 2, 4 × 0, ? 1, 2 × 0 + 2)       i.e., (2, ?1, 2).       Now required distance is the distance between points       (?1, ?5, ?10) and (2, ?1, 2)